Attack trees in Isabelle

In this paper, we present a proof theory for attack trees. Attack trees are a well established and useful model for the construction of attacks on systems since they allow a stepwise exploration of high level attacks in application scenarios. Using the expressiveness of Higher Order Logic in Isabelle, we succeed in developing a generic theory of attack trees with a state-based semantics based on Kripke structures and CTL. The resulting framework allows mechanically supported logic analysis of the meta-theory of the proof calculus of attack trees and at the same time the developed proof theory enables application to case studies. A central correctness and completeness result proved in Isabelle establishes a connection between the notion of attack tree validity and CTL. The application is illustrated on the example of a healthcare IoT system and GDPR compliance verification

Globally reasoning about localised security policies in distributed systems

In this report, we aim at establishing proper ways for model checking the global security of distributed systems, which are designed consisting of set of localised security policies that enforce specific issues about the security expected. The systems are formally specified following a syntax, defined in detail in this report, and their behaviour is clearly established by the Semantics, also defined in detail in this report. The systems include the formal attachment of security policies into their locations, whose intended interactions are trapped by the policies, aiming at taking access control decisions of the system, and the Semantics also takes care of this. Using the Semantics, a Labelled Transition System (LTS) can be induced for every particular system, and over this LTS some model checking tasks could be done. We identify how this LTS is indeed obtained, and propose an alternative way of model checking the not-yet-induced LTS, by using the system design directly. This may lead to over-approximation thereby producing imprecise, though safe, results. We restrict ourselves to finite systems, in the sake of being certain about the decidability of the proposed method. To illustrate the usefulness and validity of our proposal, we present 2 small case-study-like examples, where we show how the system can be specified, which policies could be added to it, and how to decide if the desired global security property is met. Finally, an Appendix is given for digging deeply into how a tool for automatically performing this task is being built, including some implementation issues. The tool takes advantage of the proposed method, and given some system and some desired global security property, it safely (i.e. without false positives) ensures satisfaction of it

Attack Trees in Isabelle extended with probabilities for Quantum Cryptography

In this paper, we present a proof calculus for Attack Trees and how its application to Quantum Cryptography is made possible by extending the framework to probabilistic reasoning on attacks. Attack trees are a well established and useful model for the construction of attacks on systems since they allow a stepwise exploration of high level attacks in application scenarios. Using the expressiveness of Higher Order Logic in Isabelle, we succeed in developing a generic theory of attack trees with a state-based semantics based on Kripke structures and CTL. The resulting framework allows mechanically supported logic analysis of the meta-theory of the proof calculus of attack trees and at the same time the developed proof theory enables application to case studies. A central correctness and completeness result proved in Isabelle establishes a connection between the notion of attack tree validity and CTL. Furthermore in this paper, we illustrate the application of Attack Trees to security protocols on the example of the Quantum Key Distribution (QKD) algorithm. The application motivates the extension of the Attack Tree proof calculus by probabilities. We therefore introduce probabilities to quantify finite event sequences and show how this extension can be used to extend CTL to its probabilistic version PCTL. We show on the example of QKD how probabilistic reasoning with PCTL enables proof of quantitative security properties

Distributed Differential Privacy and Applications

Recent growth in the size and scope of databases has resulted in more research into making productive use of this data. Unfortunately, a significant stumbling block which remains is protecting the privacy of the individuals that populate these datasets. As people spend more time connected to the Internet, and conduct more of their daily lives online, privacy becomes a more important consideration, just as the data becomes more useful for researchers, companies, and individuals. As a result, plenty of important information remains locked down and unavailable to honest researchers today, due to fears that data leakages will harm individuals. Recent research in differential privacy opens a promising pathway to guarantee individual privacy while simultaneously making use of the data to answer useful queries. Differential privacy is a theory that provides provable information theoretic guarantees on what any answer may reveal about any single individual in the database. This approach has resulted in a flurry of recent research, presenting novel algorithms that can compute a rich class of computations in this setting. In this dissertation, we focus on some real world challenges that arise when trying to provide differential privacy guarantees in the real world. We design and build runtimes that achieve the mathematical differential privacy guarantee in the face of three real world challenges: securing the runtimes against adversaries, enabling readers to verify that the answers are accurate, and dealing with data distributed across multiple domains